Q35 of 36 Page 110

In the given progressive wave y = 5 sin (100πt – 0.4πx) where y and x are in m, t is in s. What is the

(a) amplitude


(b) wave length


(c) frequency


(d) wave velocity


(e) particle velocity amplitude.


Equation for a progressive wave y = 5sin(100πt-0.4πx)


Comparing the equation with the general displacement equation for a progressive wave,



we have


(a) Amplitude A = 5 m


(b) k = 0.4π. k is given by the relation



where λ is the wavelength. Therefore for k = 0.4π we have



(c) The angular frequency ω = 100π. The angular frequency is given by,



where f is the frequency of the wave.



(d) The wave velocity is given by the relation,



(e) Differentiating the given equation with respect to t we get the equation for particle velocity, i.e.



Therefore, the amplitude particle velocity is given by



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If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.

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Given below are some functions of x and t to represent the displacement of an elastic wave.

(a) y = 5 cos (4x) sin (20t)


(b) y = 4 sin (5x – t/2) + 3 cos (5x – t/2)


(c) y = 10 cos [(252 – 250) πt ] cos [(252+250)πt ]


(d) y = 100 cos (100πt + 0.5x)


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For the harmonic travelling wave y = 2 cos 2π (10t–0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of,

(a) 4 m


(b) 0.5 m


(c)


(d) (at a given instant of time)


(e) What is the phase difference between the oscillation of a particle located at x = 100cm, at t = T s and t = 5 s?