Правка разделов «Statement», «Answer»
en/3.6.24.md
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| ### Statement | |||
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| + | $3.6.24.$ The compressibility of mercury, water, and air are $3\times10^{-5}$, $5\times10^{-5}$, and $0.71$ atm$^{-1}$, and their densities are $13.6\times10^3$, $1\times10^3$, and $1.2$ kg/m$^3$, respectively. | ||
| + | Determine the speed of sound in these media. | ||
| ### Solution | |||
| The speed of sound is $v=\sqrt{K/\rho}$, where $K$ and $\rho$ are the bulk modulus and the density of the medium, respectively. The bulk modulus is the reciprocal of the compressibility of the medium. Using $1$ atm $\approx10^5$ Pa, we obtain the bulk moduli of mercury, water, and air as $3.3\times10^9$, $2.0\times10^9$, and $1.4\times10^5$ Pa, respectively. Thus, the speeds of sound in these media are roughly $500$, $1400$, and $340$ m/s, respectively. | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $500$, $1400$, and $340$ m/s, respectively. | ||
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| ### Statement | ### Statement | ||
| $3.6.24.$ The compressibility of mercury, water, and air are $3\times10^{-5}$, $5\times10^{-5}$, and $0.71$ atm$^{-1}$, and their densities are $13.6\times10^3$, $1\times10^3$, and $1.2$ kg/m$^3$, respectively. | |||
| Determine the speed of sound in these media. | |||
| ### Solution | ### Solution | ||
| The speed of sound is $v=\sqrt{K/\rho}$, where $K$ and $\rho$ are the bulk modulus and the density of the medium, respectively. The bulk modulus is the reciprocal of the compressibility of the medium. Using $1$ atm $\approx10^5$ Pa, we obtain the bulk moduli of mercury, water, and air as $3.3\times10^9$, $2.0\times10^9$, and $1.4\times10^5$ Pa, respectively. Thus, the speeds of sound in these media are roughly $500$, $1400$, and $340$ m/s, respectively. | The speed of sound is $v=\sqrt{K/\rho}$, where $K$ and $\rho$ are the bulk modulus and the density of the medium, respectively. The bulk modulus is the reciprocal of the compressibility of the medium. Using $1$ atm $\approx10^5$ Pa, we obtain the bulk moduli of mercury, water, and air as $3.3\times10^9$, $2.0\times10^9$, and $1.4\times10^5$ Pa, respectively. Thus, the speeds of sound in these media are roughly $500$, $1400$, and $340$ m/s, respectively. | ||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $500$, $1400$, and $340$ m/s, respectively. | ||