Question

Standing waves on a 1.0m long string that is fixed at both ends are seen at successive frequencies of 24 hz and 36hz. what is the fundamental frequency and wave speed

Answer 1

The multiples of the fundamental frequency are the standing wave frequencies for a string.

Since 24 Hz and 36 Hz are consecutive frequencies, the fundamental frequency must be 36 −12 = 12 Hz. Meaning that the standing wave with frequency 36 Hz is the third harmonic (i.e., m = 3),

The wave speed fulfills the equation f1 = v / 2L where f1 is the fundamental frequency and L is the length of the string

So we can say that:

v = 2Lf1

= 2(1.0)(12)

= 24 m/s

 

Answer 2

We have that the fundamental frequency and wave speed  is mathematically given as

a)F= 12 Hz

b) v= 24 m/s

Fundamental frequency and wave speed

Question Parameters:

Standing waves on a 1.0m long string that is fixed at both ends are seen at successive frequencies of 24 hz and 36hz.

Generally the equation for the velocity  is mathematically given as

v = f x lamda

Therefore

f1 x lamda1 = f2x lamda2

24 x 2L/n = 36 x 2L/n+1

2/n = 3/n+1

n =2

Hence

v = 24 x 2 x 1 /2

b) v= 24 m/s

Generally the equation for the Frequency mathematically given as

F= v/2L

F= 24/2

a)F= 12 Hz

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