Question

A piano tuner hears a beat every 2.20 s when listening to a 258.0 Hz tuning fork and a single piano string. What are the two possible frequencies (in Hz) of the string? (Give your answers to at least one decimal place.)1. f = . Hz (smaller value) 2. f = Hz (larger value)

Answer 1

Smaller value = 257.55 Hz.

Larger value = 254.455 Hz.

Step-by-step explanation:

Beat : Beat is a phenomenon obtained when two notes of nearly equal frequency are sounded together. Thereafter, there is a rise and fall of intensity of sound. It is as a result of constructive interference.

±f₍b₎ = f₁ + f₂

where f₍b) = Beat frequency, f₁ = frequency of the turning fork, f₂ = frequency of the string.

T₍b₎ =beat time = 2.2 s.

Recall That,

f = 1/T

f₍b) = 1/2.2 = 0.455 Hz

The beat is formed

Either

T₍beat) = f₁ + f₂ =

0.455 = 258 + f₂

∴ f₂ = 258 - 0.455 = 257.55 Hz.

or

-T₍beat) = f₁ + f₂

f₂ = f₁ + T₍beat)

f₂ = 254 + 0.455 = 254.455 Hz.