How to re-size a sound's wave length

[BioMedPhD]

In the field of acoustical physics the mathematical relationship (wavelength (lambda) = speed of sound (velocity) / frequency (cycles per sec)) indicates that lambda (wavelength) would increase if the speed of sound were increased while the frequency (cps) is held constant (e.g., 100 Hz).

Setting aside (for the moment) the empirical issues surrounding how one increases the speed of sound while holding frequency constant, my question relates to understanding the pressure mechanics that would have to underlie such an increase in wavelength.

I’m looking for an intuitive physical explanation that starts with the idea that wave length describes the distance required for the pattern of pressure increases (condensation) and decreases (rarefaction) to repeat its self.

Doesn’t an increase in wave length mean that somewhere in this process the leading edge of the pressure wave must have selectively and spatially jumped forward relative to the trailing wave?

Really ! – How could that happen?

 

[Nugatory]

The speed of sound is different in different mediums, so the way to increase the speed of sound and hence the wavelength is to get your sound wave to stop moving through air and start moving through something else instead.

In this case, the leading edge of the pressure wave really does jump ahead relative to the trailing edge. The leading edge is traveling through the air, reaches the surface of the new medium, and starts propagating through the new medium at the new higher speed. Meanwhile, the trailing edge is still traveling through air, so is propagating at the slower speed and falls behind. When the trailing edge reaches the new medium, it also propagates at the faster speed so stops falling behind, but by then the wavelength has already been stretched out.

 

[mishima]

Wavelength changes happen at the boundaries between materials. Frequency never changes. For example, maybe a rock hammer is tapping out a regular beat underwater. It does so with a frequency of say 10 Hz. In the water, the wavelength would then be sound speed / frequency or 150 m (1497/10). Now the energy travels as a disturbance through the water up to the surface. Just because the wave has reached the surface doesn't mean the rock hammer isn't hitting the rock 10 times a second. The frequency is the same. However, since sound speed in air is different, the wavelength changes 331/10 (33 m). These are probably unrealistic numbers but you get the idea. Nothing about the material changes what is happening with the source of the wave (frequency), that would be weird/crazy if it did.

 

[BioMedPhD]

Thanks Guys - All your responses agree with my privately held rational - Thanks again

 

[PJC01]

I would approach this question by first understanding the basic principles of sound waves and how they are produced. Sound waves are longitudinal waves, meaning that they travel in the same direction as the oscillations of the particles in the medium (such as air). These oscillations create areas of high and low pressure, which we perceive as sound.

The wavelength of a sound wave is the distance between two consecutive points of the same phase, such as two consecutive compressions or rarefactions. It is directly related to the frequency of the sound, which is the number of cycles (complete oscillations) per second. The higher the frequency, the shorter the wavelength, and vice versa.

Now, to answer the question of how to increase the wavelength of a sound wave while holding frequency constant, we need to consider the equation mentioned in the content (wavelength = velocity / frequency). This equation tells us that the wavelength is inversely proportional to the frequency. In other words, as the frequency decreases, the wavelength increases.

So, to increase the wavelength of a sound wave while keeping the frequency constant, we would need to decrease the frequency of the sound. This can be achieved by either decreasing the speed of sound or increasing the medium's density.

In terms of pressure mechanics, this would mean that the particles in the medium would have to oscillate at a lower frequency, resulting in a longer distance between areas of high and low pressure. This could be achieved by increasing the distance between the particles (decreasing the density) or slowing down their movement (decreasing the speed of sound).

To address the question of how the leading edge of the pressure wave could jump forward while the trailing wave remains constant, we need to understand that sound waves are not physical objects that move from one point to another. They are simply disturbances in the medium, and the particles themselves do not move with the wave. Therefore, the concept of a leading edge jumping forward is not applicable in this scenario.

In conclusion, to increase the wavelength of a sound wave while holding frequency constant, we would need to decrease the frequency of the sound by either decreasing the speed of sound or increasing the medium's density. This would result in a longer distance between areas of high and low pressure, without any physical movement of the wave itself.