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Chapter 6: Problem 27

Describe how sound is produced in string instruments. Why does tightening a string change the frequency of the sound it makes?

Short Answer

Expert verified
Answer: Tightening a string on a string instrument increases its tension. According to the formula f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}, an increase in tension (T) leads to an increase in frequency (f) of the vibrating string. As a result, the sound produced has a higher pitch.

Step by step solution

01

Sound Production in String Instruments

Sound is produced in string instruments when the strings vibrate. When a musician plucks or bows a string, it vibrates back and forth, creating a wave. This vibration generates sound waves which travel through the air and reach our ears, allowing us to perceive the sound.
02

Frequency and Pitch

The frequency of a sound wave is the number of vibrations that occur per second, measured in hertz (Hz). The frequency of the sound produced by a vibrating string determines its pitch. Higher frequencies correspond to a higher pitch, while lower frequencies correspond to a lower pitch.
03

Tension and Sound Frequency

The frequency of the sound produced by a vibrating string depends on three factors: its length, its mass per unit length, and its tension. When a string is tightened, its tension increases. This increased tension causes the string to vibrate at a higher frequency, which in turn produces a sound of higher pitch.
04

Mathematical Relationship

The relationship between the tension (T), the mass per unit length (µ), the length (L), and the frequency (f) of a vibrating string can be described using the following formula: f = \frac{1}{2L}\sqrt{\frac{T}{\mu}} When the tension (T) increases, the frequency (f) also increases. This explains why tightening a string changes the frequency of the sound it makes.
05

Conclusion

In summary, sound is produced in string instruments by the vibration of strings. The frequency of the produced sound, which determines its pitch, depends on the tension in the string. Tightening a string increases its tension and, consequently, increases the frequency of the sound it produces, resulting in a higher pitch.

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Most popular questions from this chapter

The rays that could be used to represent the steady sound emitted by a warning siren on the top of a pole would look similar to the gravitational field lines (Section 2.8) representing the field around an object. Explain why they are alike, and point out the one important difference.

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