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# Vibrations in strings, Vibrations produced in closed pipes, Vibrations produced in open pipes

Vibration in strings

Waves travels aloog a horizontal rope fixed at one end, and the other end is free to move. Sound wave is generated from a fixed string that is allowed to move at the other end. In this mode of vibration the vibrating wire produces a sound of the lowest possible note whose frequecy is called fundamental frequency. The mode of vibration is giving rise to the fundamental mode of vibration.

The distance between the two consecutive mode is Λ/2 and this is equal to the lenght of the string l.

L = Λ/2 or Λ = 2l

For any wave we have that v = fΛ where v is the velocity, f, the frequency, and Λ the wavelenght.

Vibrations produced in closed pipes.

In a closed pipe, only odd numbers of harmonics are present as overtones accompanying the fundamental note. The possible harmonics are fо  , 3fо  , 5fо  , 7fо etc.

Where fо = fundamental frequency.  fo = v/4l

Vibrations produced in open pipes

In an open pipe the harmonics present are 2fо, 3fо, 4fо,5fо etc. , thet is, both odd and even harmonics are present as overtones. fo = v/2l

EVALUATION

1. The shortest lenght of the air column in a resonance tube closed at one end which resonates to a frequency of 560Hz is found to be 20cm. What is the wavelenght of this sound in air?

2. Determine the frequency of the first overtone of a closed pipe of lenght 30cm, if the end correction is 0.8cm and the velocity of sound is 340m/s.

General revision

1. An electric heater immersed in some water raises the temperature of the water from 400C   to 1000C in 6min. After another 25min, it is noticed that half the water has boiled away. Ignoring heat lost to the surrounding, calculate the specific  latent heat of vaporisation of water.

2. The image of an object is located 6cm behind a convex mirror. If its magnification is 0.6, calculate the focal length of the mirror.

WEEKEND ASSIGNMENT

1  The natural frequency of a simple pendulum depends only on

A area B amplitude C length D speed

2  A tuning fork sounds louder when its stem is pressed against a table top than when held in    air because

A. a larger mass of air is set vibrating by the table top  B. the whole table vibrates in resonance

C. the whole table has acquire a larger frequency  D.  the fork and the table have the same     frequency

3 What type of motion does the skin of a talking drum perform when it is being struck with     drumstick      A. random B. rotational C. vibratory D. translational

4   Which of the following statement is not true

A. musical notes consists of combination of sounds of regular frequency

B. sound travels faster in solids than in gases

C. the loudness of sound is determine by its frequency

D. the pitch of a note depend on the frequency of vibration of the source

5 Calculate the wavelength  of a note which is one octave lower than a note of  256 Hz  in a    medium  in which the speed of sound is 352m/s      A. 0.69m B. 1.38m C .  2.75m  D.  5.50m

THEORY

1 What do you understand by the term resonance?

2 An object 5cm high is placed at a distance of 12cm from a convex lens of focal length 8cm, calculate the position and nature of the image produced.