An oscillator of frequency `680 Hz` drives two speakers . The speakers are fixed on a vertical pole at a distance `3 m` from each other as shown in Fig. 7.103. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and speed of sound is `v = 340 m//s` , answer the following questions.

At some instant , when the person is at a distance `4 m` from the pole , the wave function ( at the person's location) that describes the waves coming from the lower speaker `y = A cos (kx - omega t)` , where `A` is the amplitude , `omega = 2 pi v` with `v = 680 Hz` (given) and `k = 2 pi//lambda`
Wave function ( at the person's location) that describes waves coming from the upper speaker can be expressed as :

Options

A. ` y = A cos ( kx - omega t + pi)`
B. `y = A cos ( kx - omega t + pi//2)`
C. `y = A cos ( kx - omega t + 2pi)`
D. `y = A cos ( kx - omega t + (3 pi)/(2))`

Answer

C

Explanation

When the person is at distance `4 cm` from pole then the path travelled by wave from `s_(2) = 5 m`.
`:.` Path differnce `= 5 - 4 = 1m`
As ` Delta x = n lambda , lambda = (1)/(2) m`
`n = (1)/(lambda) = 2`
Therefore , path difference ` = 1m = 2 lambda`.
Path difference of `2 lambda` corresponds to `4 pi`
`y = A cos ( kx - omega t + 4 pi)`
It can be expressed as
`y = A cos ( kx - omega t + 2 pi)`