Time interval between two successive maxima of sound waves with frequencies v1 and v2 is given bya)v1/v2b)1/ (v1- v2)c)v1= v2= 0d)v1- v2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

As we know time interval will have dimensions of time so check in option for dimension of time.
Dimensions of v is "per second" or [T^-1]

Answer

Explanation:

Let us assume that the two successive maxima of sound waves with frequencies v1 and v2 are observed at intervals of time t1 and t2, respectively.

Therefore, the time interval between two successive maxima can be given as:

t = t2 - t1

Now, we know that the time period of a wave is given as the time taken by a wave to complete one oscillation. Therefore, the time period of sound wave with frequency v1 can be given as:

T1 = 1/v1

Similarly, the time period of sound wave with frequency v2 can be given as:

T2 = 1/v2

Now, let us assume that the two successive maxima of sound waves with frequencies v1 and v2 coincide at a particular instant of time. Therefore, the time interval between two successive maxima can be given as:

t = T1 = T2

Substituting the values of T1 and T2, we get:

t = 1/v1 - 1/v2

On simplifying the above equation, we get:

t = (v2 - v1)/v1v2

Therefore, the time interval between two successive maxima of sound waves with frequencies v1 and v2 is given by option B:

t = 1/(v1 - v2)

Answer

Two ways to solve this question

FIRST METHOD

U have to know that this is talking about interference of two sound waves of different frequencies.

let the waves be

Asin(w1t + kx). and. Asin(w2t + kx)

where w1 and w2 are there angular frequencies

so there phase difference is
(w1 - w2)t = 2π(v1 - v2)t

as w= 2πv. v is frequency

now for maxima phase difference= 2nπ for n=0,1,2,3....

first maxima (n=0)

0 = (w1-w2)t1

so t1 =0

2nd maxima (n=1)

2π = 2π(v1 - v2)t2

so t2 = 1/(v1 - v2)

3rd maxima (n=2)

4π = 2π(v1 - v2)t3

so t3 = 2/(v1 - v2)

and so on

now time interval between two successive maxima is

t2-t1 or t3-t2 which is = 1/(v1 - v2)

SECOND METHOD

this is easier

as we know time interval will have dimensions of time

so check in option for dimension of time.

(dimension of v is 'per second')

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