Which one of these statements regarding standing waves on a string is FALSE
Select one:
a. The frequency of the first harmonic depends on the tension in the string
b. The frequency of the first harmonic depends on the speed of the wave
c. The frequency does not depend on the length of the string
d. The frequency of the first harmonic depends on the mass per unit length of the string
The false statement is: c. The frequency does not depend on the length of the string.
To determine which statement regarding standing waves on a string is false, let's analyze each option:
a. The frequency of the first harmonic depends on the tension in the string.
This statement is true. The frequency of the first harmonic, also known as the fundamental frequency, is directly proportional to the tension in the string. If the tension increases, the frequency also increases.
b. The frequency of the first harmonic depends on the speed of the wave.
This statement is false. The frequency of the first harmonic is determined by the length of the string, not the speed of the wave. The speed of the wave depends on the tension and the mass per unit length of the string.
c. The frequency does not depend on the length of the string.
This statement is false. The frequency of the first harmonic is inversely proportional to the length of the string. As the length of the string increases, the frequency decreases.
d. The frequency of the first harmonic depends on the mass per unit length of the string.
This statement is true. The frequency of the first harmonic is inversely proportional to the mass per unit length of the string. If the mass per unit length increases, the frequency decreases.
Therefore, the false statement is:
b. The frequency of the first harmonic depends on the speed of the wave.