Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 93

A sound wave is observed to travel through a liquid with a speed of $1500 \mathrm{m} / \mathrm{s}$. The specific gravity of the liquid is 1.5 Determine the bulk modulus for this fluid.

Short Answer

Expert verified
The bulk modulus of the fluid is \(3.375 * 10^9\) Pa.

Step by step solution

01

Identify knowns

We know the speed of the sound wave \(v = 1500\) m/s and the specific gravity of the fluid \(SG = 1.5\). We also know the acceleration due to gravity \(g = 9.81\) m/s².
02

Recall the specific gravity definition

The specific gravity of a substance is the ratio of its density to the density of water at 4 degrees Celsius, which is roughly 1000 kg/m³. Hence we can determine the density of the fluid \(\rho\) as \(SG * \rho_{water} = 1.5 * 1000\) kg/m³ = 1500 kg/m³.
03

Use the formula of sound speed in a fluid

The speed of sound in a fluid is given by the formula \(v = \sqrt{\frac{K}{\rho}}\), where \(K\) is the bulk modulus which we are trying to find. We rearrange this to get \(K = v^2 * \rho\).
04

Substitute the values into the equation

Substituting the values we obtained before and given in the problem, we get \(K = (1500)^2 * 1500\) Pa.
05

Calculate the bulk modulus

Calculate the above expression to obtain the bulk modulus \(K = 3.375 * 10^9\) Pa.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A compressed air tank in a service station has a volume of \(10 \mathrm{ft}^{3} .\) It contains air at \(70^{\circ} \mathrm{F}\) and 150 psia. How many tubeless tires can it fill to 44.7 psia at \(70^{\circ} \mathrm{F}\) if each tire has a volume of 1.5 \(\mathrm{ft}^{3}\) and the compressed air tank is not refilled? The tank air temperature remains constant at \(70^{\circ} \mathrm{F}\) because of heat transfer through the tank's large surface area.

The universal gas constant \(R_{0}\) is equal to \(49,700 \mathrm{ft}^{2} /\left(\mathrm{s}^{2} \cdot^{\circ} \mathrm{R}\right)\) or \(8310 \mathrm{m}^{2} /\left(\mathrm{s}^{2} \cdot \mathrm{K}\right) .\) Show that these two magnitudes are equal.

A stick of butter at \(35^{\circ} \mathrm{F}\) measures 1.25 in. \(\times 1.25\) in. \(x\) 4.65 in. and weighs 4 ounces. Find its specific weight.

A regulation basketball is initially flat and is then inflated to a pressure of approximately \(24 \mathrm{lb} / \mathrm{in}^{2}\) absolute. Consider the air temperature to be constant at \(70^{\circ} \mathrm{F}\). Find the mass of air required to inflate the basketball. The basketball's inside radius is 4.67 in.

At what atmospheric pressure will water boil at \(35^{\circ} \mathrm{C} ?\) Express your answer in both SI and BG units.
See all solutions

Recommended explanations on Physics Textbooks

Further Mechanics and Thermal Physics

Read Explanation

Electromagnetism

Read Explanation

Circular Motion and Gravitation

Read Explanation

Linear Momentum

Read Explanation

Magnetism

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free