A student was investigating the difference in wavelength of a bass guitar and a whistle. The student noticed that the frequency of the whistle was high, and the bass guitar had a low frequency. Given the students' information and the model below, what is the difference in wavelength for each instrument and explain how frequency affects the wavelength?
The difference in wavelength between the bass guitar and the whistle is primarily determined by their difference in frequency.
Frequency refers to the number of complete cycles of a wave that occur in one second. It is measured in Hertz (Hz). A higher frequency means more cycles occur in a given time period.
Wavelength, on the other hand, refers to the distance between two corresponding points on a wave, such as from one peak to the next or from one trough to the next. It is commonly represented by the Greek letter lambda (λ) and is measured in meters (m). In simpler terms, it represents the spatial length of one cycle of the wave.
In general, there is an inverse relationship between frequency and wavelength - as frequency increases, wavelength decreases, and vice versa. Mathematically, this relationship can be expressed by the equation:
Wavelength = Speed of wave / Frequency
Given that the frequency of the whistle is high and the bass guitar has a low frequency, this indicates that the whistle has a shorter wavelength compared to the bass guitar. The whistle produces a higher-pitched sound with more cycles occurring per second, resulting in a shorter wavelength.
On the other hand, the bass guitar produces a lower-pitched sound with fewer cycles occurring per second, resulting in a longer wavelength.
Therefore, the difference in wavelength for each instrument can be observed as a tangible difference in pitch or tone. The whistle would have a shorter wavelength, associated with a higher frequency, while the bass guitar would have a longer wavelength, associated with a lower frequency.