(15.15) where, as before, C is the undetermined constant from dimensional analysis. The ecact deriation shows that c=1. Thus, the general formula for longitudind waves in a medium is:
v=ρB
Arswer Mass per untt length of the wire, For a linear medium, like a solid bar, the elasticlty is Young's modulus. which has the same dimension as the Bulk modulus. Dimensional analysis for this case is the same
16.4.2 Speed of a Lon 4 longitudinal waves in a solid bar is given by
(Speed of Sound) v=ρY (15itudinal Wave
In a longitudinal wave, the constituents of the where Y is the Youngs modinus of the material medlum oscillate forward and backward in the of the bar. Table 15.1 gives the rpeed of sound direction of propagation of the wave. We have In some media. already seen that the sound waves travel in the Table 15.1 speed of Saund in some Media form of compressions and rarefactions of small volume elements of air. The elastic property that determines the stress under compressional strain is the bulk modulus of the medium deflned by (see Chapter 9 )
B=−ΔV/VΔP
Here, the change in pressure ΔP produces a volumetric strain VΔV′. Bhas the same dimension as pressure and given in SI units in terms of pascal ( Pa. The inertial property relevant for the propagation of wave is the mass density ρ, with dimensions [ML−3]. Simple inspection reveals that quantity B/p has the relevant dimension:
$$
\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}{\left[\mathrm{ML}^{-3}\right]}=\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right]
$$
(15.17) Liquids and solids generally have higher speed of sound than gases. [Note for solids, the speed be are considered to be the only referred to is the speed of longltudinal Thus, if B and ρ are considered to be the onty waves in the solid. This happens because they relevant physical quantities.

Question

(15.15) where, as before, C is the undetermined constant from dimensional analysis. The ecact deriation shows that c=1. Thus, the general formula for longitudind waves in a medium is:
v=ρB​​
Arswer Mass per untt length of the wire, For a linear medium, like a solid bar, the elasticlty is Young's modulus. which has the same dimension as the Bulk modulus. Dimensional analysis for this case is the same
16.4.2 Speed of a Lon 4 longitudinal waves in a solid bar is given by
(Speed of Sound) v=ρY​​ (15itudinal Wave
In a longitudinal wave, the constituents of the where Y is the Youngs modinus of the material medlum oscillate forward and backward in the of the bar. Table 15.1 gives the rpeed of sound direction of propagation of the wave. We have In some media. already seen that the sound waves travel in the Table 15.1 speed of Saund in some Media form of compressions and rarefactions of small volume elements of air. The elastic property that determines the stress under compressional strain is the bulk modulus of the medium deflned by (see Chapter 9 )
B=−ΔV/VΔP​
Here, the change in pressure ΔP produces a volumetric strain VΔV′​. Bhas the same dimension as pressure and given in SI units in terms of pascal ( Pa. The inertial property relevant for the propagation of wave is the mass density ρ, with dimensions [ML−3]. Simple inspection reveals that quantity B/p has the relevant dimension:
$$
\frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}{\left[\mathrm{ML}^{-3}\right]}=\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right]
$$
(15.17) Liquids and solids generally have higher speed of sound than gases. [Note for solids, the speed be are considered to be the only referred to is the speed of longltudinal Thus, if B and ρ are considered to be the onty waves in the solid. This happens because they relevant physical quantities.

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Question Text	(15.15) where, as before, $C$ is the undetermined constant from dimensional analysis. The ecact deriation shows that $c = 1$ . Thus, the general formula for longitudind waves in a medium is: $v = \frac{B}{ρ}$ Arswer Mass per untt length of the wire, For a linear medium, like a solid bar, the elasticlty is Young's modulus. which has the same dimension as the Bulk modulus. Dimensional analysis for this case is the same 16.4.2 Speed of a Lon 4 longitudinal waves in a solid bar is given by (Speed of Sound) $v = \frac{Y}{ρ}$ (15itudinal Wave In a longitudinal wave, the constituents of the where $Y$ is the Youngs modinus of the material medlum oscillate forward and backward in the of the bar. Table $15.1$ gives the rpeed of sound direction of propagation of the wave. We have In some media. already seen that the sound waves travel in the Table $15.1$ speed of Saund in some Media form of compressions and rarefactions of small volume elements of air. The elastic property that determines the stress under compressional strain is the bulk modulus of the medium deflned by (see Chapter 9 ) $B = - \frac{Δ P}{Δ V / V}$ Here, the change in pressure $Δ P$ produces a volumetric strain $\frac{Δ V ^{'}}{V}$ . Bhas the same dimension as pressure and given in SI units in terms of pascal ( $Pa$ . The inertial property relevant for the propagation of wave is the mass density $ρ$ , with dimensions $[ML^{- 3}]$ . Simple inspection reveals that quantity $B / p$ has the relevant dimension: \[ \frac{\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]}{\left[\mathrm{ML}^{-3}\right]}=\left[\mathrm{L}^{2} \mathrm{~T}^{-2}\right] \] (15.17) Liquids and solids generally have higher speed of sound than gases. [Note for solids, the speed be are considered to be the only referred to is the speed of longltudinal Thus, if $B$ and $ρ$ are considered to be the onty waves in the solid. This happens because they relevant physical quantities.
Updated On	Feb 12, 2023
Topic	Waves and SHM
Subject	Physics
Class	Class 12
Answer Type	Video solution: 1
Upvotes	68
Avg. Video Duration	2 min

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