The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?
The tension needed to tune the given string is .
The frequency of the lowest note on a piano is .
The mass of the string is .
As the vibrating section of the string is long, the two ends of this vibrating wire are fixed, and the string is vibrating in the fundamental harmonic with wavelength
The wave speed along the string is
The linear density is given by
The wave speed is also given by .
Substitute the given values
Therefore, the tension in the string is .
Traditional Indonesian music uses an ensemble called a gamelan that is based on tuned percussion instruments somewhat like gongs. In Bali, the gongs are often grouped in pairs that are slightly out of tune with each other. When both are played at once, the beat frequency lends a distinctive vibrating quality to the music. Suppose a pair of gongs are tuned to produce notes at 151 Hz and 155 Hz. How many beats are heard if the gongs are struck together and both ring for 2.5 s?
Two loudspeakers emit sound waves of the same frequency along the x-axis. The amplitude of each wave is a. The sound intensity is minimum when speaker 2 is 10 cm behind speaker 1. The intensity increases as speaker 2 is moved forward and first reaches maximum, with amplitude 2a, when it is 30 cm in front of speaker 1. What is
a. The wavelength of the sound?
b. The phase difference between the two loudspeakers?
c. The amplitude of the sound (as a multiple of a) if the speakers
are placed side by side?
Two microwave signals of nearly equal wavelengths can generate a beat frequency if both are directed onto the same microwave detector. In an experiment, the beat frequency is 100 MHz. One microwave generator is set to emit microwaves with a wavelength of 1.250 cm. If the second generator emits a longer wavelength, what is that wavelength?
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