Ch 17: Superposition

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 17: Superposition

Problem 19

Chapter 17, Problem 19

A bass clarinet can be modeled as a 120-cm-long open-closed tube. A bass clarinet player starts playing in a 20° C room, but soon the air inside the clarinet warms to where the speed of sound is 352m/s . Does the fundamental frequency increase or decrease? By how much?

Verified step by step guidance

Step 1: Understand the problem. The bass clarinet is modeled as an open-closed tube, meaning it has one open end and one closed end. The fundamental frequency of such a tube is determined by the speed of sound in the air and the length of the tube. The formula for the fundamental frequency is:

f = \frac{v}{4 L}

, where

v

is the speed of sound and

L

is the length of the tube.

Step 2: Identify the given values. The length of the tube is

L = 120 cm

(convert to meters:

L = 1.2 m

). The speed of sound changes from its value at 20°C (approximately

v = 343 m / s

) to

v = 352 m / s

as the air warms.

Step 3: Analyze the relationship between the speed of sound and the fundamental frequency. Since the fundamental frequency is directly proportional to the speed of sound (

f \propto v

), an increase in the speed of sound will result in an increase in the fundamental frequency.

Step 4: Calculate the initial fundamental frequency using the formula

f = \frac{v}{4 L}

. Substitute

v = 343 m / s

and

L = 1.2 m

into the equation.

Step 5: Calculate the new fundamental frequency using the same formula, but with

v = 352 m / s

. Compare the two frequencies to determine the increase in the fundamental frequency. The difference between the two frequencies will give the amount by which the fundamental frequency increases.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Fundamental Frequency

The fundamental frequency is the lowest frequency at which a system, such as a musical instrument, vibrates. For an open-closed tube like a bass clarinet, the fundamental frequency is determined by the length of the tube and the speed of sound in the medium inside it. It can be calculated using the formula f = v / (4L), where f is the frequency, v is the speed of sound, and L is the length of the tube.

Speed of Sound

The speed of sound is the rate at which sound waves propagate through a medium. In air, this speed is influenced by temperature; as the temperature increases, the speed of sound also increases. In this scenario, the speed of sound in the bass clarinet is given as 352 m/s, which is higher than the typical speed at room temperature, indicating that the air inside the instrument has warmed up.

Effect of Temperature on Frequency

Temperature affects the speed of sound, which in turn influences the frequency of sound produced by musical instruments. As the speed of sound increases due to a rise in temperature, the fundamental frequency of the instrument also increases. Therefore, in this case, as the air inside the bass clarinet warms up, the fundamental frequency will increase, leading to a higher pitch.

Recommended video:

Guided course

07:40

The Doppler Effect

Related Practice

Textbook Question

Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm. What is the wavelength of the sound?

views

Textbook Question

A 170-cm-long open-closed tube has a standing sound wave at 250 Hz on a day when the speed of sound is 340m/s . How many pressure antinodes are there, and how far is each from the open end of the tube?

views

Textbook Question

The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0°C helium. What is its frequency when filled with 0°C air?

views

Textbook Question

A carbon dioxide laser is an infrared laser. A CO₂ laser with a cavity length of 53.00 cm oscillates in the m=100,000 mode. What are the wavelength and frequency of the laser beam?

Textbook Question

Two loudspeakers in a 20°C room emit 686 Hz sound waves along the x-axis. If the speakers are out of phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum constructive?

views

Textbook Question

The lowest note on a grand piano has a frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400 g. The vibrating section of the string is 1.90 m long. What tension is needed to tune this string properly?

views