Creating musical sounds
Creating musical sounds

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Creating musical sounds

5.14 Response and damping

You have learned so far in this chapter that when a musician plays an instrument, they force the primary vibrator to vibrate. If the primary vibrator is driven at one of its resonance frequencies, the normal mode of vibration corresponding to that resonance frequency will be excited. Now, in practice it is also true to say that even if the primary vibrator is driven at a frequency close to the resonance frequency, the normal mode will still be excited, but just to a lesser degree. In other words, there is a range of frequencies over which the normal mode will be excited.

This is depicted graphically in Figure 22, which shows a frequency-response curve, also sometimes referred to as a resonance curve, for the first mode of vibration of an instrument. As the frequency at which the primary vibrator is driven is increased, the resulting standing wave increases in amplitude then decreases. The amplitude of the standing wave is largest when the primary vibrator is forced to vibrate at exactly the resonance frequency fR.

Figure 22
Figure 22 Frequency-response curve for the first mode of vibration of an instrument. The resonance frequency is fR and the sharpness of the frequency response can be expressed as f″−f

The sharpness of the frequency response is often expressed in terms of the range of frequencies over which the amplitude of vibration is greater than half the amplitude at resonance, i.e. the width of the resonance peak at half its height. For example, in Figure 22, the sharpness of the frequency response is equal to f″−f′.

Figure 23
Figure 23 Frequency-response curves showing the first mode of vibration for both lightly and heavily damped primary vibrators

If energy is supplied to the instrument in a short burst, the primary vibrator will be set vibrating but the vibrations will gradually die away because of damping. The damping is a measure of how rapidly the system loses energy through friction or by radiating the energy away as sound, etc. If the damping is light, the vibrations will continue for a long time. It turns out that lightly damped primary vibrators have a narrow frequency response. If the damping is heavy, on the other hand, the vibrations will die away quickly, and heavily damped primary vibrators have a broad frequency response. Figure 23 shows frequency-response curves for the first mode of vibration of a lightly damped primary vibrator (solid line) and of a heavily damped primary vibrator (dashed line).

The curves shown in Figure 22 and Figure 23 show the frequency response of only a single mode of vibration. If the frequency range is extended upwards to take in more modes of vibration, the frequency-response curve will contain several peaks – each peak being at the frequency of a mode of vibration (see Figure 24).

Figure 24
Figure 24 Frequency-response curve showing three modes of vibration of a primary vibrator

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371