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A cylindrical tube open at both ends has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now………

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Explanation

$ {f_L \over f_S } = { \nu + \nu_L \over \nu + \nu_S } $ using this equation the frequency of reflected sound heard by the girl, $ f_L = { \nu + \nu_L \over \nu -\nu_S} f_S $

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Three sound waves of equal amplitudes have frequencies (v-1 ), v, ( v+1). They superpose to give beats. The number of beats produced per second will be …….

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Explanation

$ f_{open} = { \nu \over 2l_ {open} } $ $ f_{closed } = { \nu \over 4 l_{closed} = { \nu \over 4l_{open} /2 } $ $ [ As l_{closed} = { l_{open} \over 2 } ]$ $ = {\nu \over 2 l_{open} = f_{open} $ i.e. frequency remains unchanged.

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A wave travelling along the x-axis is described by the equation y(x,t) = 0.005Cos(áx - ât). If the wavelength and the time period of the wave are 0.08 m and 2.0 s respectively, then á and â in appropriate units are ………

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Explanation

If we assume that all the three waves are in same phase at t = 0, we shall hear only 1 beat $s^{-1}$

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A wave travelling along a string is described by the equation y= A Sin(ùt-kx). The maximum particle velocity is ………..

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Explanation

$ y (x, t) = 0.005 cos ( \alpha x - \beta t) $ compare it with standard equation $ y (x,t ) = A cos (kx -wt ) = A cos \left( { 2 \pi \over \lambda } = - { 2 \pi \over T }t \right) $ $ \therefore \alpha = { 2 \pi \over \lambda } and \beta = { 2 \pi \over T } $

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Two tuning forks P and Q when set vibrating gives 4 beats/second. If the prong of fork P is filed, the beats are reduced to 2/s. What is the frequency of P, if that of Q is 250 hz.?

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The length of a string tied across two rigid supports is 40 cm. The maximum wavelength of a stationary wave that can be produced in it is… cm.

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Explanation

For a string tied between two fixed supports, the longest (or maximum) wavelength of a stationary wave that can be produced is twice the length of the string. Given the length of the string is 40 cm, the maximum wavelength is: $$ ext{Wavelength} = 2 imes 40 ext{ cm} = 80 ext{ cm}$$

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A stationary wave of frequency 200 hz are formed in air. If the velocity of the wave is 360 m/s, the shortest distance between two antinodes is …….m

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A tuning fork produces 8 beats per second with both 80 cm and 70 cm of stretched wire of a sonometer. Frequency of the fork is …….hz.

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An open pipe is in resonance in 2nd harmonic with frequency f . Now one end of the tube is closed and frequency is increased to f2, such that the resonance again occurs in the nth harmonic. Choose the correct option.

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Explanation

When an open pipe is in resonance in its 2nd harmonic, the frequency is given by $f = rac{2v}{2L}$, where $L$ is the length of the pipe. If one end of the pipe is closed, the pipe behaves like a closed pipe, and the nth harmonic for a closed pipe is given by the odd harmonics (1, 3, 5, ...). For the pipe to resonate again, the frequency must be adjusted. For $n = 5$, the frequency $f_2$ would be $ rac{5v}{4L}$. Therefore, $f_2 = rac{5}{4} f$. Hence, the correct option is $n = 5, f_2 = (5 / 4) f_1$.

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Assertion – Reason type questions : For the following questions, statement as well as the reason(s) are given. Each questions has four options. Select the correct option. Statement – 1: Two waves moving in a uniform string having uniform tension cannot have different velocities. Statement – 2 : Elastic and inertial properties of string are same for all waves in same string. Moreover speed of wave in a string depends on its elastic and inertial properties only.

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