Speed of Waves

The speed of a wave on a string is $150$ m/s when the tension is $120$ N. The percentage increase in the tension to raise the wave speed by $20\%$ is

A wire is under tension of $2$ kg wt and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increase in tension is (in kg wt)

What is the effect of humidity on sound waves when humidity increases?

The velocity of sound in air is doubled when the temperature is raised from $0^\circ\text{C}$ to $\alpha^\circ\text{C}$. The value of $\alpha$ is ______.

A string of length $0.5$ m and mass $10^{-3}$ kg is tightly clamped at its ends. The tension in the string is $0.8$ N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t$. What is the minimum value of $\Delta t$ which allows constructive interference between successive pulses?

Two monoatomic ideal gases '1' and '2' of molecular masses $m_1$ and $m_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas '1' to that in gas '2' is

The ratio of the speed of sound in helium gas to that in nitrogen gas at $295$ K is ( Ratio of specific heats $\gamma$ for helium is $\frac{5}{3}$ and that for nitrogen is $\frac{7}{5}$. Molecular weight for helium and nitrogen are $4$ and $28$ respectively.)

The enclosed air inside a closed box of rigid walls has pressure $P_1$. The density of air inside this box is constant. On heating the gas, the pressure of the enclosed air is increased from $P_1$ to $P_2$. Now it is observed that the sound travels $1.4$ times faster than at pressure $P_1$. The ratio $P_2$ by $P_1$ is

Two strings $(A, B)$ having linear densities $\mu_A = 2 \times 10^{-4}\text{ kg/m}$ and, $\mu_B = 4 \times 10^{-4}\text{ kg/m}$ and lengths $L_A = 2.5\text{ m}$ and $L_B = 1.5\text{ m}$ respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1/t_2$ is:

A uniform rope of mass $0.1$ kg and length $2.5$ m hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point $0.5$ m distance from lower end will be ($g = 10$ m/s$2$)

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius of cross section R is $v_1$, and that in the other string having radius of cross section R/2 is $v_2$. Then $\frac{v_2}{v_1}$ =

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A: A sound wave has higher speed in solids than gases.

Reason R: Gases have higher value of Bulk modulus than solids.

In the light of the above statements, choose the correct answer from the options given below

A string of mass 0.2 Kg is under a tension of 2.5 N. The length of the string is 2 m. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is

The speed of sound in oxygen at S.T.P. will be approximately: (given, $R = 8.3\text{ JK}^{-1},\ \gamma = 1.4$)

A steel wire with mass per unit length $7.0 \times 10^{-3}\text{ kg m}^{-1}$ is under tension of $70\text{ N}$. The speed of transverse waves in the wire will be:

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

A uniform wire $20\text{ m}$ long and weighing $50\text{ N}$ hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity $= g = 10\text{ ms}^{-2}$)

A tuning fork of frequency $220\text{ Hz}$ produces sound waves of wavelength $1.5\text{ m}$ in air at N.T.P. The increase in wavelength when the temperature of air is $27^\circ\text{C}$ is nearly $\left(\sqrt{\frac{300}{273}} = 1.05\right)$

A wire $PQ$ has length $4.8\text{ m}$ and mass $0.06\text{ kg}$. Another wire QR has length $2.56\text{ m}$ and mass $0.2\text{ kg}$. Both wires have same radii and are joined as a single wire. This wire is under tension of $80\text{ N}$. A wave pulse of amplitude $3.5\text{ cm}$ is sent along the wire $PQ$ from end $P$. the time taken by the wave pulse to travel along the wire from point P to R is?

A uniform rope of length '$L$' and mass '$m_1$ ' hangs vertically from a rigid support. A block of mass '$m_2$' is attached to the free end of the rope. A transverse wave of wavelength '$\lambda_1$' is produced at the lower end of the rope. The wavelength of the wave when it reaches the top of the rope is '$\lambda_2$'. The ratio $\frac{\lambda_1}{\lambda_2}$ is

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is

An organ pipe filled with a gas at 27$^\circ$C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90$^\circ$C, the resonance frequency at the same mode will be

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by 4%, will be __________%.

The wavelength of sound in any gas depends upon

What is the effect of pressure on the speed of sound in a medium, if pressure is doubled at constant temperature?

A uniform rope of length $12\text{ m}$ and mass $6\text{ kg}$ hangs vertically from the rigid support. A block of mass $2\text{ kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\text{ m}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is

A uniform metal wire has length $L$, mass $M$ and density $\rho$. It is under tension $T$ and $v$ is the speed of transverse wave along the wire. The area of cross-section of the wire is

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104 N. When the tension is changed to T, the velocity changed to v/2. The value of T is close to:

The extension in a wire obeying Hooke's law is $x$. The speed of sound in the stretched wire is $v$. If the extension in the wire is increased to $4x$, then the speed of sound in a wire is

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope?

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm2) is 90 ms-1. If the Young's modulus of wire is 16 $\times$ 1011 Nm-2, the extension of wire over its natural length is:

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms${}^{-1}$. When the car has acceleration a, the wave-speed increases to 60.5 ms${}^{-1}$. The value of a, in terms of gravitational acceleration g, is closest to:

The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2, corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is 0°C. On some other day, when temperature is T, the speed of sound produced by the same blade and at the same frequency is found to be 336 ms–1. Approximate value of T is

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 $\times$ 103 kg/m3 and its Young’s modulus is 9.27 $\times$ 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations?

A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength $\lambda$1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda$2. The ratio $\lambda$ 2/$\lambda$1 is

A uniform string of length $20\text{ m}$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is: (take $g = 10\text{ ms}^{-2}$)

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K${}^{-1}$ mol${}^{-1}$. If the speed of sound in this gas at NTP is 952 m s${}^{-1}$, then the heat capacity at constant pressure is

(Take gas constant R $=$ 8.3 J K${}^{-1}$ mol${}^{-1}$)

The temperature at which the speed of sound becomes double as was at $27^\circ\text{C}$ is

A $5.5$ metre length of string has a mass of $0.035\text{ kg}$. If the tension in the string in $77\text{ N}$, the speed of a wave on the string is

The velocity of sound in any gas depends upon