Standing-wave vibrations are set up in a crystal wine glass with four nodes and four antinodes equally spaced around the 2.80-cm radius of the rim.If the resonant frequency of the glass is 8.50 kHz,what is the speed of the transverse waves moving around the glass?
A)1 500 m/s
B)748 m/s
C)374 m/s
D)238 m/s

Question

Quizplus · Accepted Answer

The resonant frequency of the glass is given by:

f = (v/λ)

where v is the speed of the transverse waves around the glass and λ is the wavelength of the standing wave.

We can find the wavelength from the distance between nodes or antinodes, which is half of the wavelength:

λ = 2(2.80 cm) = 5.60 cm = 0.0560 m

Substituting the values:

8.50 kHz = (v/0.0560 m)

v = (8.50 kHz)(0.0560 m) = 0.476 m/s

Therefore, the speed of the transverse waves moving around the glass is:

v = 748 m/s (rounded to three significant figures)

Standing-Wave Vibrations Are Set Up in a Crystal Wine Glass