Two tuning forks are sounded together. One has a frequency of 741 Hz and the other a frequency of 715 Hz. Calculate the beat frequency that would be produced.
x = sin (2pi*741t)
y = sin (2pi*715t)
x+y= sin (2pi*741t)+sin(2pi*715t)
but
sin a + sin b= 2 sin.5(a+b)cos.5(a-b)
so
x+y =2 [sin average] cos half difference
every max of the cosine, either + or - is a big noise so what you hear if they are close is the average frequency times the difference frequency
741 - 715 = 26 Hz
To calculate the beat frequency produced by two tuning forks with different frequencies, you need to find the difference between their frequencies. In this case, the beat frequency can be calculated by subtracting the frequency of one tuning fork from the frequency of the other tuning fork.
Beat frequency = |f1 - f2|
Where:
f1 = frequency of one tuning fork (in Hz)
f2 = frequency of the other tuning fork (in Hz)
In this case, f1 = 741 Hz and f2 = 715 Hz.
Beat frequency = |741 Hz - 715 Hz|
Beat frequency = 26 Hz
Therefore, the beat frequency produced by the two tuning forks is 26 Hz.