Question

Two violin strings are tuned to the same frequency 294 H. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together?

Answer 1

Answer:

Beat frequency together = 2.95 Hz (Approx)

Explanation:

Given:

Frequency (F) = 294 H

Decrease in tension = 2%

Find:

Beat frequency together

Computation:

Tension = (100 - 2) / 100

Tension (T) = 0.98

Beat frequency together = Frequency (F) - (√T × F)

Beat frequency together = 294 - (√0.98 × 294)

Beat frequency together = 2.95 Hz (Approx)

Answer 2

The beat frequency heard when the two strings are played together is 2.95 Hz.

Given data:

The tuning frequency of the violin is, f = 294 Hz.

Decrement in the tension is, 2 %.

Since, tension is reduced at the rate of 2%. Then the new magnitude of tension on the string is,

T = (100 - 2 )/100

T = 0.98

Then the expression for the beat frequency heard when the two strings are played together is given as,

$f_{b}=f -(\sqrt{T \times f})$

Solving as,

$f_{b}=294-(\sqrt{0.98 \times 294})\\\\f_{b}=2.95\;\rm Hz$

Thus, we can conclude that the beat frequency heard when the two strings are played together is 2.95 Hz.

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