Physics‎ > ‎

Sound of Music.

posted Oct 11, 2016, 1:03 PM by Upali Salpadoru   [ updated Oct 15, 2016, 2:30 PM ]


When you sing, you begin with Do, Re, Mi..”“ Do, Re, Mi..”

“ Do, Re, Mi..

The first three notes just happen to be  ‘Do, Re, Mi”

“ Do, Re, Mi…...Do, Re, Mi, Fa, So, La, Ti..

Fig.1. She plucks the strings with one hand while she presses the strings with the fingers of the other.

We use  sounds for signalling and communications. Music is produced only when the notes are arranged in a way soothing or pleasant to a listener.

A note in music may mean the pitch of the wave. There are high pitch notes and low pitch notes. In key boards, such as a piano, as you move to the right, the pitch gets higher.

The pitch of a note depends on the frequency of vibration.

The loudness or volume depends on the amplitude.


Fig.2. In a musical keyboard the frequency increases to the right.

String instruments

These produce musical notes with stretched strings. When a tight sering is plucked. It vibrates for a while emitting a continuous sound, This is a kind of resonance due to the forming of a standing wave.

The factors that determine the frequency are the length of the string, the tension and the thickness


Fig.3. Sonometer is an instrument to study vibrations in strings.

When a vibrating tuning fork is kept on the box a section of spring can be made to vibrate due to resonance. The weights and the length L of the wire can be altered easily.

Vibrations can easily be detected by placing bits of folded paper on the wire. When the wire vibrates they get thrown off.

Longer strings give low notes.  Low pitch...................Frequency is inversely proportional to length.

Tighter strings  give high notes.  High pitch............... F  pr.jpg√ T

Thicker strings produce  low notes.  Low pitch.

A vibrating string has a transverse wave motion. It gives rise to a longitudinal wave in air.

The frequency remains unaltered while the wavelength changes. This is due to the change in velocity.


Fig.4. Formula for the frequency of a vibrating string.

2L is used as the fundamental of a string is twice the length. (Refer to the table below)


Fig.5 Fundamental note and the overtones.

The string column in the table shows 3 ways of vibrating a string. The first one gives the fundamental note while the others are called overtones or harmonics.

A musical note produced by a string will be a blend of the fundamental and several harmonics.


Fig.6. Red and blue show two harmonics (overtones)  The resulting wave can be obtained by adding the amplitudes of those. This is shown as black dots.

This is the reason for the difference in tone or colour  in different instruments. This is described as timbre.

Practice Problem.1.

A stretched wire 1.00 m. Long resonates to a tuning fork of 260 Hz.

  1. Calculate the wavelength  of the fundamental?.  

  2. Find the velocity of the transverse wave.

      3.    If the velocity in air is 340 ms-1 calculate the wavelength of the  sound.


  1. λ = 2L…………= 2.00m  (Fundamental wave of a wire is twice the length)

  2. V. of wire - f*λ.  …………   V= 260 x 2.0…….V=   520 ms-1.

  3. V. in air = F *λ. ………  340 = 260 x λ.

                                             λ= 340/60

                                               = 5.67 m.


What happens when two waves of different frequency interfere?

You get what are known as ‘beats’; a note of changing amplitude; soft sound alternating with loud ones.

Bts 1.jpg

C- Constructive interference.

D- Destructive interference.

Antinode- Loud sound.

Node- Soft sund.

  1. Sound wave 1.

  2. Sound wave 2.

1+2. Beat wave.

The difference in the frequencies of two pure notes gives the beat frequency.

Beat frequency = Frequency 1 - Frequency 2.    Ie; ......... f b = f1 - f2.

Most musical instruments produce beats which are much appreciated. This is due to the blending of the fundamental with the harmonics.


1 1. 1. A hunter fires a shot near a river bank. There are 3 listeners keeping the same distance from the source of sound. How would they  hear the sound ?

A- The bird in a tree will hear first.

B - A rabbit sleeping will hear first.

C-  A fish will hear first.

D-  All will hear at the same time.

2. There are four statements regarding the wavelength of a sound wave. Select the correct one?

A- Depends entirely on the energy given to the wave.

B- Equal to half the length of a vibrating string.

C- Decreases with the thickness of a stretched wire.

D- Changes with the temperature.

For 3.and 4.

Each compression on a longitudinal wave corresponds to what point on a transverse wave?

a. Crests b.   amplitude c.   troughs D, wavelength.

4. A wire, stretched by a weight of a sonometer, is made to resnate to a tuning fork of 250 Hz. The adjusted length of the vibrating section was 0.5m long.

3. What is the wavelength?

250x2 m.  b.  0.5x2 m.  c. 0.5 ÷ 2 . d. 0.5 m.

4. If the vibrating length is changed 0.8m, what would be the required frequency fr it to resonate?

A.156.Hz.  b. 250   c.400 Hz   d. 125 Hz.

5. Danny wants to make a musical instrument using steel wires.

He plans to use these methods to vary the pitch.

1. Using wires of different materials.
2. Using different lengths.
3. Changing the tension
4. Using  tuning forks of different pitch.

.A. All are correct.              B. Only 2 and 3 are correct.

C. Only  4 is correct.         D. Only 4 is wrong.

5x5 = 25 marks.

Q. 2.0

A pipe open at both ends vibrates at fundamental at 150 Hz.

2.1. If the length of the pipe is L what would be its fundamental wavelength?

2.2. Taking the speed of sound as 340ms-1, calculate the wavelength.

2.3 What could be the length of the pipe?

2.4 What is the frequency at the next harmonic?