A vibrating sonometer wire emits a note which gives a beat frequency of 6Hz when sounded unison with a loaded tunning fork of frequency 257Hz. When the fork is loaded, the beat frequency increases. What is the frequency of the note emitted by the sonometer?
To find the frequency of the note emitted by the sonometer, we'll need to use the concept of beat frequency.
First, let's understand what beat frequency is. When two waves with slightly different frequencies interfere with each other, they produce a pattern of constructive and destructive interference. This pattern creates a perceived fluctuation in the volume of the combined sound, known as a beat. The beat frequency is the difference in frequency between the two sound sources.
In this case, we have two frequencies: the frequency of the loaded tuning fork (257Hz) and the beat frequency (6Hz) when sounded unison with the vibrating sonometer wire.
To calculate the frequency of the note emitted by the sonometer, we can subtract the beat frequency from the frequency of the tuning fork:
Frequency of the note emitted = Frequency of the tuning fork - Beat frequency
Frequency of the note emitted = 257Hz - 6Hz
Frequency of the note emitted = 251Hz
Therefore, the frequency of the note emitted by the sonometer is 251Hz.