Wave on a String Revision Notes - IIT JEE/NEET Preparation | Nucleon

## Wave on a String

• WAVES
• Wave motion is the phenomenon that can be observed almost everywhere around
us, as well it appears in almost every branch of physics. Surface waves on bodies
of matter are commonly observed. Sound waves and light waves are essential to
our perception of the environment. All waves have a similar mathematical
description, which makes the study

• TYPES OF MECHANICAL WAVES
• Mechanical waves can be classified according to the physical properties of the medium, as well
as in other ways

• DESCRIBING WAVES
• Two kinds of graph may be drawn - displacement-distance and displacement-time.
A displacement - distance graph for a transverse mechanical wave shows the displacement y of
the vibrating particles of the transmitting medium at different distance x from the source at a
certain instant i.e. it is like a photograph showing shape of the wave at that particular instant.

• WAVE LENGTH, FREQUENCY, SPEED
• If the source of a wave makes f vibrations per second, so too will the particles of the transmitting medium.
That is, the frequency of the waves equals frequency of the source.
When the source makes one complete vibration , one wave is generated and the disturbance spreads out
a distance ? from the source. If the source continues to vibrate with constant frequency f, then f waves will
be produced per second and the wave advances a distance f ? in one second. If v is the wave speed then

• TRAVELLING SINE WAVE IN ONE DIMENSION (WAVE ON STRING)
• well as for longitudinal waves.
A complete description of the wave requires specification of f(x). The most important case, by far, in
physics and engineering is when f(x) is sinusoidal, that is,

• THE LINEAR WAVE EQUATION
• The transverse velocity and transverse acceleration of any point on the string do not reach their maximum
value simultaneously. Infact, the transverse velocity reaches its maximum value (?A) when the displacement

• THE SPEED OF TRANSVERSE WAVES ON STRINGS
• where T is tension in the string (in Newtons) and ? is mass per unit length of the
string (kg/m)

• POWER TRANSMITTED ALONG THE STRING BY A SINE WAVE
• When a travelling wave is established on a string, energy is transmitted along the direction
of propagation of the wave, in form of potential energy and kinetic energy

• THE PRINCIPLE OF SUPERPOSITION
• When two or more waves simultaneously pass through a point, the disturbance at the point is given by the
sum of the disturbances each wave would produce in absence of the other wave(s).

• INTERFERENCE OF WAVES GOING IN SAME DIRECTION
• Suppose two identical sources send sinusoidal waves of same angular frequency ? in positive
x-direction. Also, the wave velocity and hence, the wave number k is same for the two waves.

• REFLECTION AND TRANSMISSION OF WAVES
• A travelling wave, at a rigid or denser boundary, is reflected with a phase reversal but the
reflection at an open boundary (rarer medium) takes place without any phase change. The
transmitted wave is never inverted, but propagation constant k is changed.

• STANDING WAVES
• Suppose two sine waves of equal amplitude and frequency propagate on a long string in opposite directions.
The equations of the two waves are given by

• Fixed at one end
• Standing waves can be produced on a string which is fixed at one end and whose other end
is free to move in a transverse direction. Such a free end can be nearly achieved by connecting
the string to a very light thread

• LAWS OF TRANSVERSE VIBRATIONS OF A STRING - SONOMETER WIRE
• LAWS OF TRANSVERSE VIBRATIONS OF A STRING - SONOMETER WIRE

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