1. A string is stretched between fixed supports separated by 73.0 cm. It is obse

Question

1. A string is stretched between fixed supports separated by 73.0 cm. It is observed to have resonant frequencies of 310 and 465 Hz, and no other resonant frequencies between these two.

(a) What is the lowest resonant frequency for this string? __Hz

(b) What is the wave speed for this string? __m/s

2. Organ pipe A, with both ends open, has a fundamental frequency of 300 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. Use 343 m/s for the speed of sound in air.

(a) How long is pipe A? ___m

(b) How long is pipe B? ___m

Explanation / Answer

1)

a)

L = length

n = nth mode

nth frequency is given as

fn = nV/(2L) = 310                                        eq-1

similarly

fn+1 = (n + 1)V/(2L) = 465                                        eq-2

Taking ratio of eq-1 and eq-2

n/(n + 1) = 310/465

n = 2

f = lowest frequency = fn/n = 310/2

f = 155 Hz

b)

wave speed is given as

V = 2Lf

V = 2 x 0.73 x 155

V = 226.3 m/s

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