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Velocity of wave in stretched string is given by, where, T is the tension, and m is the mass per unit length. If is length of string then time taken by wave to reach the other end of string is, We have, Therefore, Time taken to reach the other end of the string is,

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Waves

A string of mass 2.50 kg is under the tension of 200N. The length of the stretched string is 20.0m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

Velocity of wave in stretched string is given by,



where,

T is the tension, and

m is the mass per unit length.

If $Error converting from MathML to accessible text.$ is length of string then time taken by wave to reach the other end of string is,

We have,



Therefore,

Time taken to reach the other end of the string is,

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A stone dropped from top of the tower 300 m high splashes into water of pond near the base of tower. When is the splash heard at the top? Velocity of sound in air = 340m/s, g = 9.8 m/s².

Let t be the time taken by stone to reach the surface of water in pond.

When the stone strikes the surface of water, splash is produced.

Let, t₂ be the time taken by the splash to reach top of tower.

The total time after which the splash is heard after dropping the stone is,

t = t₁ + t₂The stone is dropped from height 300m.

The time taken by the stone to reach the surface of water can be calculated by using the thrid equation of motion,

The time taken by splash to reach the top of tower is,

Therefore, total time taken to hear the splash at the top is,

Total time

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A transverse harmonic wave on a string is described by

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where x, y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling or a stationary wave? If this is travelling, then what is the speed and direction of its propagation?
(b) What is its amplitude and frequency?
(c) What is the initial phase at the origin?
(d) What is the least distance between two successive crests in the wave?

The harmonic wave equation is given by,

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...(1)

The general harmonic wave equation is,

straight y left parenthesis straight x comma space straight t right parenthesis space equals space straight A space sin left parenthesis ωt minus kx plus straight ϕ right parenthesis

...(2)

Comparing (1) and (2), we get

Amplitude space of space the space wave comma space straight A equals 3.0 cm comma space Angular space frequency comma space straight omega equals 36 space rad divided by straight s Wave space vector comma space straight k space equals space 0.018 space cm to the power of negative 1 end exponent

(a) The given wave is a travelling wave.

The speed of wave is,

space space space straight v equals straight omega over straight k equals fraction numerator 36 over denominator 0.018 end fraction equals 20000 cm divided by straight s equals 20 straight m divided by straight s

(b) Amplitude, A = 3.0cm

Frequency,

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straight ϕ equals straight pi divided by 4

(d) The least distance between two successive crests in the wave is equal to wavelength.

straight lambda equals fraction numerator 2 straight pi over denominator straight k end fraction equals fraction numerator 22 over denominator 7 cross times 0.018 end fraction cm almost equal to 3.5 straight m

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Use the formula v =

square root of γP over straight rho end root

to explain why the speed of sound in air:

(a) is independent of pressure,

Take the relation:

v = √γP/ρ ...(i)

where,

Density, ρ = Mass/Volume = M/V

M = Molecular weight of the gas

V = Volume of the gas
Hence, equation (i) reduces to:

v = √γPV/M ...(ii)

Now from the ideal gas equation for n = 1:

PV = RT

For constant T, PV = Constant

Since both M and γ are constants, v = Constant

Hence, at a constant temperature, the speed of sound in a gaseous medium is independent of the change in the pressure of the gas.

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A steel wire has a length of 12.0m and mass 2.10kg. What should be the tension in wire so that the speed of transverse wave on the wire equals to the speed of sound in dry air at 20°C i.e. 343 m/s?

Velocity of wave in stretched string is given by,

where,

M is the mass and L is the length of wire

We have,

Velocity of sound,

Mass of steel wire, M = 2.1kg
Length of the string, L = 12m

Therefore,

Tension in the wire is,

287 Views