Problem 26 - Chemistry The Science in Context

Question

In the 1990 s the Russian and American navies developed extremely low- frequency communications networks to send messages to submerged submarines. The frequency of the carrier wave of the Russian network was \(82 \mathrm{Hz}\), whereas the Americans used \(76 \mathrm{Hz}\) a. What was the ratio of the wavelengths of the Russian network to the American network? b. To calculate the actual underwater wavelength of the transmissions in either network, what additional information would you need?

Step-by-Step Solution

Answer

Answer: The ratio of the wavelengths of the Russian and American networks is 38/41 or approximately 0.9268. To calculate the actual underwater wavelengths, we need to know the speed of the wave in the underwater environment.

Step 1: Find the relation between frequencies and wavelengths

Since the speed of the wave is constant for both networks, we can express the relation between the wavelengths of the Russian and American networks as follows: \(\frac{λ_R}{λ_A} = \frac{f_A}{f_R}\) where \(λ_R\) and \(λ_A\) are the wavelengths of the Russian and American networks, respectively, and \(f_R\) and \(f_A\) are the corresponding frequencies.

Step 2: Calculate the ratio of the wavelengths

Given the frequencies of the Russian and American networks (\(f_R = 82 Hz\) and \(f_A = 76 Hz\)), we can calculate the ratio of the wavelengths: \(\frac{λ_R}{λ_A} = \frac{76}{82} = \frac{38}{41}\) Therefore, the ratio of the wavelengths for the Russian network to the American network is \(\frac{38}{41}\) or approximately 0.9268.

Step 3: Determine the additional information needed to calculate the actual wavelengths

To calculate the actual underwater wavelength of the transmissions in either network, we need to know the speed of the wave (\(v\)) in the underwater environment. The speed of electromagnetic waves in different mediums (air, water, etc.) can vary. Thus, knowing the speed of the wave in the underwater environment, we can use the formula \(λ = \frac{v}{f}\) to find the actual wavelengths for each network.

Key Concepts

Wavelength and Frequency Relationship

When it comes to understanding how submarine communications work, it's imperative to grasp the intrinsic connection between wavelength and frequency. These two properties of waves are inviolably linked by the formula \( v = f \lambda \), where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength.

Simply put, if you know the frequency of a wave and the medium through which it travels, you can determine its wavelength, and vice versa. In the context of submarine communications, lower frequencies, like those used by the Russian and American navies, come with longer wavelengths. This relationship is crucial because longer wavelengths can penetrate deeper into the water, making them ideal for reaching submerged submarines.

However, while frequency and wavelength are inversely proportional — meaning that as one increases, the other decreases — the speed of wave propagation in a given medium remains constant. Thus, by knowing the frequencies used by the Russian (82 Hz) and American (76 Hz) networks, we can derive the ratio of their wavelengths. As evidenced by the provided exercise, the wavelengths are related by the inverse of the frequency ratio: \( \frac{\lambda_R}{\lambda_A} = \frac{f_A}{f_R} \) which yields approximately 0.9268 for the given frequencies.

Electromagnetic Wave Propagation

Diving deeper into the phenomenon of submarine communications brings us to the concept of electromagnetic wave propagation. For electromagnetic waves, such as radio waves used in communication networks, the propagation can considerably differ based on the medium through which the waves are traveling.

The speed of electromagnetic waves is the fastest in a vacuum, such as space, where it traverses at approximately 299,792 kilometers per second. When these waves enter a medium like water, their speed is significantly reduced due to the medium's density and electromagnetic properties. This reduction affects how we calculate the wavelength for use in certain applications like submarine communications.

Understanding Medium Impact

In water, the electromagnetic waves adjust to the conditions, which involve absorption and scattering effects, ultimately influencing how far and how clearly the signal can be received. It's for this reason that additional information, such as the specific speed of wave propagation in underwater conditions, is imperative for calculating the actual wavelengths of the transmissions from both the American and Russian networks, as mentioned in the solution.

Underwater Communication

Now, let's focus on the specifics of underwater communication, which presents unique challenges due to the aquatic environment. In the realm of submarine communication, the frequency of the transmitted waves is a critical factor to consider. Lower frequencies, such as the 76 Hz and 82 Hz used by the American and Russian navies respectively, penetrate the deep waters more efficiently than higher frequencies, which are more susceptible to attenuation.

Water, being a more dense medium than air, requires special consideration in terms of communication technology. The primary issue is the attenuation of electromagnetic waves. As water molecules absorb and scatter the electromagnetic waves, high-frequency signals quickly lose their strength over distance. Therefore, submarines use extremely low-frequency (ELF) waves to ensure that the message reaches great depths without significant loss of signal strength.

Practical Implications

Moreover, the equipment used for ELF communication must be capable of generating and receiving such low-frequency signals, which necessitates large antennas and high-powered transmitters. This form of communication has its trade-offs, as the data rate for ELF signals is relatively low, which limits the complexity and length of the communication sent to submarines. Considering the critical need for reliable communication with submerged submarines, understanding these nuances of underwater communication is essential for maintaining the effectiveness and security of naval operations.