A piano tuner hears a beat every 2.20 s when listening to a 266.0 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.)

The lower frequency is

The higher frequency is  

Explanation:

From the question we are told that

     The period is  

      The frequency of the tuning fork is  

Generally the beat frequency is mathematically represented as

substituting values

Since the beat  frequency is gotten from the beat produced by the tuning fork and and  the string   then

The possible frequency of the string ranges from

to

Now  substituting values

For  

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we need to know the time interval during which the force acts. impulse of force = momentum change