Physics with Application; Acoustics; Trumpet

In summary, we discussed the concept of a hearing trumpet and its shape, which is a flared funnel. We then looked at its dimensions, with a diameter of 8 cm at the wide end and 0.7 cm at the narrow end. The question posed was how much the hearing trumpet increases the intensity of sound and by how many decibels. We used the equations for intensity, power, and intensity level to find the solution, which involves finding the areas at the input and output ends of the trumpet.
  • #1
MAtkinson
4
0
From Acoustics, Resonance, Energy, Power, Intensity and The Doppler Effect

Homework Statement



An old-fashioned hearing trumpet has the shape of a flared funnel, with a diameter of 8 cm at its wide end and a diameter of 0.7 cm at its narrow end. Suppose that all of the sound energy that reaches the wide end is funneled into the narrow end. By what factor does this hearing trumpet increase the intensity of sound (measured in W/m2)? By how many decibels does it increase the intensity level of sound?


Homework Equations



Intensity = Power / Area

Intensity = Energy / (Time)*(Area)

Intensity Level = 10*Log(Intensity/10^(-12)) (db)

The Attempt at a Solution



...
 
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  • #2
Welcome to PF!
We have a policy of ignoring questions where there is no attempt made on the problem. But I can make an exception since it is your first post, and offer a suggestion to get you started.

Start by finding the areas, at the input end and at the output to ear end. Put them into your formulas.
 
  • #3
... Thanks for the insightful reply. I understand it's not the most difficult question, nonetheless I am getting stuck.

10^((deltaIntensityLevel)/10-12)=Power/DeltaCircleArea
 
  • #4
I don't understand that at all.
Were you able to find the two areas?
Maybe use intensity = power/area twice, once for each end.
 
  • #5


I would approach this problem by first understanding the concepts of acoustics, resonance, energy, power, intensity and the Doppler effect. Acoustics is the study of sound and its properties, including how it travels through different mediums and how it interacts with objects. Resonance is the phenomenon where an object vibrates at its natural frequency when exposed to a sound wave of the same frequency. Energy is the ability to do work, and in acoustics, it is the energy carried by sound waves. Power is the rate at which energy is transferred, and it is measured in watts (W). Intensity is a measure of the amount of sound energy passing through a unit area, and it is measured in watts per square meter (W/m2). The Doppler effect is the change in frequency of a sound wave as the source or observer moves.

Now, applying these concepts to the problem at hand, we can calculate the intensity of sound at the wide end of the hearing trumpet using the equation Intensity = Power / Area. Since all of the sound energy is funneled into the narrow end, the area at the wide end (A1) is equal to the area at the narrow end (A2). Therefore, we can rewrite the equation as Intensity = Power / (A1 + A2).

Next, we need to calculate the ratio of the areas (A1/A2) to determine the factor by which the intensity is increased. Using the given diameters, we can calculate the areas as A1 = π*(0.04m)^2 = 0.005m2 and A2 = π*(0.0035m)^2 = 3.85x10^-5m2. Therefore, the ratio of the areas is A1/A2 = 0.005/3.85x10^-5 = 130.

This means that the hearing trumpet increases the intensity of sound by a factor of 130. To calculate the increase in intensity level, we can use the equation Intensity Level = 10*log(Intensity/10^-12). Plugging in the calculated intensity (130W/m2), we get an intensity level of about 130dB. This means that the hearing trumpet increases the intensity level of sound by 130 decibels.

In conclusion, the old-fashioned hearing trumpet increases the intensity of sound by a factor of 130 and the intensity level by
 

1. What is the physics behind the sound production in a trumpet?

The sound production in a trumpet is based on the principles of acoustics. When the player blows air into the mouthpiece, it creates vibrations in the air column inside the trumpet. These vibrations are amplified and modified by the shape and size of the trumpet, producing different pitches and tones.

2. How does the design of a trumpet affect its sound?

The design of a trumpet, including the shape, size, and materials, can greatly impact its sound. The length of the trumpet's tubing determines the fundamental pitch, while the shape of the bell affects the tone quality. The materials used in the construction of the trumpet also play a role in the sound, as different materials have different resonance properties.

3. How does the player's technique affect the sound of a trumpet?

The player's technique, including their embouchure (mouth position), breath control, and finger placement, can greatly influence the sound of a trumpet. Different techniques can produce variations in pitch, tone, and volume, allowing the player to create a wide range of sounds on the trumpet.

4. What is the role of acoustics in trumpet playing?

Acoustics plays a crucial role in trumpet playing. Understanding the physics behind sound production and how the design of the trumpet affects the sound can help players improve their tone and control. Additionally, knowledge of acoustics can help players make adjustments to their technique to achieve desired sounds.

5. How does a trumpet produce different notes and pitches?

The length of the trumpet's tubing and the player's technique determine the pitch of a note. By changing the tension and position of their lips, the player can produce different notes within the range of the trumpet. The valves on the trumpet also allow the player to change the length of the tubing and produce different pitches.

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