A piano tuner sounds two strings simultaneously. One has been previously tuned t

Question

A piano tuner sounds two strings simultaneously. One has been previously tuned to vibrate at 284.0 Hz. The tuner hears 5.0 beats per second. The tuner increases the tension on the as-yet untuned string, and now when they are played together the beat frequency is 1.3 s?1.     (a) What was the original frequency of the untuned string?
1      Hz

    (b) By what percentage did the tuner increase the tension on that string?
2     %     (a) What was the original frequency of the untuned string?
1      Hz

    (b) By what percentage did the tuner increase the tension on that string?
2     %

Explanation / Answer

no. of beats heard is the difference of the frequencies at which each of the string vibrates.

if the frequency at which the second one vibrates is greater than that of the first one , once increased the no. of beats heard would increase . so , the frequency of the second one is less than that of the first one (say n)

1) 284 -- n = 5

n =279hz

2)after increasing 284 -- n1 =1.3

n1 = 282.7hz

(n1 -- n)/279 = .013

hence, it is 1.3%

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