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in Physics by (80.8k points)

Two separate strings of the same thickness are stretched so that they experience the same tension. String B is twice as dense as String A. String A, of length L, is vibrated at the fundamental frequency. How long is String B if it has the same fundamental frequency as String A?

(a) ½ L

(b) L/2

(c) L

(d) 2L

1 Answer

+1 vote
by (52.5k points)
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Best answer

The correct option is: (b) L/2

Explanation:

The Fundamental is given by

 and the velocity is given by

 

2x the density means 2x the m/L so that the velocity of the second string is smaller compared to the first string by v2 = v1 / √2. The first string length is L1 = 2f/v1, the second string length is L2 = 2f/(v1 / √2). So comparing the two we have L2 = L1 / √2

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