Dalip Saini said:Homework Statement
40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is[/B]
A
16 Hz
B
8 Hz
C
32 Hz
D
2 Hz
E
4 Hz
Homework Equations
f = v/2L
because its fundamental
The Attempt at a Solution
I thought all one had to do was (320)/2(40) = 4Hz, but the answer is 2Hz. I don't understand why
Standing waves are a type of wave pattern that occurs when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. They are classified based on the number of nodes and antinodes present in the wave.
The frequency of a standing wave is determined by the length of the medium and the speed of the wave. It can be calculated using the formula f=nv/2L, where n is the number of nodes, v is the wave speed, and L is the length of the medium.
The frequency of a standing wave and its harmonics are directly related, with each harmonic having a frequency that is a multiple of the fundamental frequency. For example, the second harmonic has a frequency that is two times the fundamental frequency.
Standing waves and their frequencies play a crucial role in the production of sound in musical instruments. The unique frequencies of standing waves in instruments like strings and pipes determine the pitch of the sound produced.
The frequency of a standing wave can be affected by factors such as the length of the medium, the speed of the wave, and the tension or density of the medium. In addition, any changes in these factors can result in a change in the frequency of the standing wave.