A 1.0 m long string is fixed at both ends and has a tension of 80N. The mass of the string
is 2 gm. Find the third harmonic of the sound emitted by this string.
a. 50 Hz
b. 100 Hz
c. 200Hz
d. 300 Hz
I found the velocity for the string. Now what?
100
To find the third harmonic of the sound emitted by the string, we need to know the speed of the waves along the string. The speed of waves on a string can be calculated using the formula:
v = √(T/μ)
where v is the speed of the wave, T is the tension in the string, and μ is the mass per unit length of the string.
In this case, the tension T is given as 80N and the mass per unit length μ is given as 2 gm. However, we need to convert the mass per unit length to kg/m to match the SI units of the other variables.
1 gm = 0.001 kg
So, 2 gm = 0.002 kg
Now, we can substitute the values into the formula:
v = √(80/0.002)
v = √40000
v = 200 m/s
The speed of the wave along the string is 200 m/s.
To find the frequency of the third harmonic, we can use the equation:
f = (3v)/(2L)
where f is the frequency, v is the speed of the wave, and L is the length of the string.
Substituting the values:
f = (3 * 200)/(2 * 1.0)
f = 600/2
f = 300 Hz
Therefore, the third harmonic of the sound emitted by this string is 300 Hz.
The correct answer is d. 300 Hz.