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Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced PDF Download

Speed of Transverse Motion

On a stretched string v = √(T/m)

where, T = tension in the string and m = mass per unit length of the string.

Speed of transverse wave in a solid v = √(η/ρ)

where, η is modulus of rigidity and ρ is density of solid.

Plane Progressive Simple Harmonic Wave

Equation of a plane progressive simple harmonic wave

Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced
or  Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced 

where,

  • y = displacement,
  • a = amplitude of vibration
  • λ = wavelength of wave, of particle,
  • T = time period of wave,
  • x = distance of particle from the origin and
  • u = velocity of wave.

 Important Relation Related to Equation of Progressive Wave

Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced
where.  Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced ts culled propagation constant of wave motion.
Wavelength,  Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced
Time period.  Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced
Frequency, Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced

Phase of the vibration is the angle of sine m equation, to plan progressive wave. It is denoted by φ.

Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced 

Relation between phase difference and path difference and time difference

Speed of a Travelling Wave & Equation of Progressive Wave | Physics for JEE Main & Advanced

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FAQs on Speed of a Travelling Wave & Equation of Progressive Wave - Physics for JEE Main & Advanced

1. What is the speed of a traveling wave?
Ans. The speed of a traveling wave is the rate at which the wave propagates through a medium. It is determined by the frequency and wavelength of the wave, and it can be calculated by multiplying the frequency with the wavelength.
2. How can the speed of a traveling wave be calculated?
Ans. The speed of a traveling wave can be calculated by multiplying the frequency of the wave with its wavelength. The formula to calculate the speed of a wave is: speed = frequency x wavelength.
3. What is the equation of a progressive wave?
Ans. The equation of a progressive wave describes the relationship between the displacement of the wave and its position. It is typically represented by the equation: y = A sin(kx - ωt), where y represents the displacement, A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time.
4. How can the speed of a wave be determined from its equation?
Ans. The speed of a wave can be determined from its equation by comparing the coefficients of x and t. The coefficient of x represents the wave number (k), while the coefficient of t represents the angular frequency (ω). The speed of the wave can then be calculated by dividing the angular frequency by the wave number.
5. What factors affect the speed of a traveling wave?
Ans. The speed of a traveling wave is influenced by two main factors: the frequency and the wavelength of the wave. As the frequency increases, the speed of the wave also increases. Similarly, as the wavelength increases, the speed of the wave decreases.
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