Which one of the following statements about standing waves on a string is FALSE?
Select one:
a. All other frequencies are integer multiples of the first harmonic
b. The first harmonic is the lowest frequency standing wave that can be formed.
c. The first harmonic has the shortest wavelength of the harmonic series
d. A set of standing waves with fixed frequencies are possible
The FALSE statement about standing waves on a string is:
c. The first harmonic has the shortest wavelength of the harmonic series
To determine which statement is false, let's examine each option and analyze them:
a. All other frequencies are integer multiples of the first harmonic
This statement is true. When forming standing waves on a string, all other frequencies (harmonics) are indeed integer multiples of the first harmonic. For example, the second harmonic is twice the frequency of the first harmonic, the third harmonic is three times the frequency, and so on.
b. The first harmonic is the lowest frequency standing wave that can be formed.
This statement is also true. The first harmonic, also known as the fundamental frequency, is the lowest frequency standing wave that can be formed on a string. It is the mode of vibration with the longest wavelength and the lowest energy.
c. The first harmonic has the shortest wavelength of the harmonic series
This statement is false. The first harmonic actually has the longest wavelength in the harmonic series. As the harmonics increase, their wavelengths decrease, meaning that the higher harmonics have shorter wavelengths.
d. A set of standing waves with fixed frequencies is possible
This statement is true. Standing waves on a string can have fixed frequencies. Each harmonic corresponds to a specific frequency, and these frequencies can be produced by setting the string into different modes of vibration.
Therefore, the FALSE statement is c. The first harmonic has the shortest wavelength of the harmonic series. The correct statement is that the first harmonic has the longest wavelength in the harmonic series.
Jake, what do you think the answer is?
Look at pictures of waves on a string.
which is the longest wave? Do waves get longer or shorter as the frequency and number of the harmonic go up?