Understanding Longitudinal Waves
A longitudinal wave involves particle motion parallel to the wave's direction of travel. Think of sound travelling through air.
Key Concepts: Compression and Rarefaction
- Compression: Areas where particles are close together, causing higher density/pressure.
- Rarefaction: Areas where particles are spread apart, causing lower density/pressure.
Wavelength in Longitudinal Waves
The wavelength, often symbolized as $\lambda$, is a fundamental measure of a wave. For longitudinal waves, it's specifically defined as the spatial period of the wave.
It is precisely the distance measured between:
- Two consecutive compressions (peaks of density/pressure).
- OR Two consecutive rarefactions (troughs of density/pressure).
This distance represents one full cycle of the wave disturbance.
Similar Questions
- A broadcasting station transmits waves with a frequency of $71 \times 10^4\ Hz$ and a speed of $3 \times 10^8\ m/s$. The wavelength of the wave is:
- A sound wave has a frequency of 4 kHz and a wavelength of 25 cm. How much time will it take to travel a distance of 2.5 km?
Important Questions from Waves
Which of the following is related to Doppler effect?
- The velocity v(x) of a particle moving in one dimension is given by v(x) = v 0 sin \(\rm\left(\frac{\pi x}{x_0}\right) \) , where v 0 and x 0 are positive constants of appropriate dimensions. If the particle is initially at x/x 0 = ϵ, where |ϵ| ≪ 1, then, in the long time, it
The position of a particle in one dimension changes in discrete steps. With each step it moves to the right, however, the length of the step is drawn from a uniform distribution from the interval \(\left[ {{\rm{λ }}\,{\rm{ - }}\,\frac{{\rm{1}}}{{\rm{2}}}{\rm{w,}}\,{\rm{λ }}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{2}}}{\rm{w}}} \right] \) , where λ and w are positive constants. If X denotes the distance from the starting point after N steps, the standard deviation \(\sqrt {\left\langle {{X^2}} \right\rangle \, - {{\left\langle X \right\rangle }^2}} \) for large values of N is
A particle of mass m in one dimension is in the ground state of a simple harmonic oscillator described by a Hamiltonian \(\frac{{{{\rm{P}}^{\rm{2}}}}}{{{\rm{2m}}}}{\rm{ + }}\frac{{\rm{1}}}{{\rm{2}}}{\rm{m}}{{\rm{\omega }}^{\rm{2}}}{{\rm{x}}^{\rm{2}}} \) in the standard notation. An impulsive force at time t = 0 suddenly imparts a momentum P0 = \(\sqrt {{\rm{hm\omega }}} \) to it. The probability that the particle remains in the original ground state is
In an elastic scattering process at an energy E, the phase shifts satisfy δ 0 ≈ 30°, δ 1≈ 10°, while the other phase shifts are zero. The polar angle at which the differential cross-section peaks is closest to
