Problem 3 A string of length 2 m with both end fixed is pluced. It is known that

Question

Problem 3 A string of length 2 m with both end fixed is pluced. It is known that the standing wave produced with 6 nodes (between two ends) has a frequency 150 Hz higher than the standing wave produced with 4 nodes (between two ends) (a) What is the first harmonic frequency (also known as the fundamental frequency)? (b) What is the frequency of the standing wave produced with 4 nodes (between two ends)? (c) Which harmonic is the standing wave produced with 4 nodes (between two ends)? (d) How fast can a wave (not the standing wave) travel on this string?

Explanation / Answer

(a) we know that frequency is given by
f = nV/2L
where n is integer , V is speed and L is the length
Now 4 nodes means 3rd harmonic
3V/2L = F -------------(1)
and for 6 nodes means 5th harmonic
5V/2L = F+150 --------------(2) (given in question)
Dividing 2 by 1
F = 225 Hz
hence fundamental frequency
V/2L = 225/3 = 75 Hz
(b) We have already calculated it as 225 Hz
(c) 4 nodes means 3 antinodes therefore it will 3rd harmonic
(d) V/2L = 75
V = 75*(2*2) = 300 m/s

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